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<h3>Titration curves</h3>

<p>Titration curves are only of interest
to explore under what conditions a titration can be made.
For example to find out what are the lower limits
for the reagent concentrations.</p>
<p style="margin-top: 1 ex">
<ul type="square">
  <li><b><a href="#Acid-base">Acid-base</a></b></li>
  <li><b><a href="#Mg-edta">Mg with <i>edta</i></a></b></li>
  </ul>
</p>
<a name="Acid-base"></a>
<hr><!-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -->


<h3>Acid-base titrations</h3>

<p>Acid-base titration curves are plots of calculated pH as a funtion of added
acid <nobr>(H<sup>+</sup>)</nobr> or base <nobr>(OH<sup>&#8722;</sup>).</nobr></p>

<p>Because the components in the <a href="DB_0_Main.htm">DATABASE</a> database
are the un-protonated ligands, you might need to
<a href="S_Modify_Chem_System.htm">exchange a component for a complex</a> if you
wish to simulate the titration of an acid (a protonated ligand) with a base.</p>

<p>For example: titration of <b>acetic acid</b> with NaOH. In order to have
<nobr>OH<sup>&#8722;</sup></nobr> as the component in
the <i>X</i>-axis it is necessary to set the hydroxide ion as a chemical component.
This is achieved by <a href="S_Modify_Chem_System.htm">exchanging a component
with a reaction.</a> In this case the original component <nobr>H<sup>+</sup></nobr>
is exchanged for the complex <nobr>OH<sup>&#8722;</sup>.</nobr> Acetate,
<nobr>CH<sub>3</sub>COO<sup>&#8722;</sup></nobr> is also exchanged with acetic
acid, <nobr>CH<sub>3</sub>COOH.</nobr>
<a name="StrongAcid"></a>
Now it is possible to calculate a titration curve of acetic acid:
<center>
<img src="images/Titration_acetic.gif" alt="Titration_acetic" title="Titration_acetic" height="221" width="302" border="1">
</center>
</p>
<p>In this example the X-axis starts at <nobr>[OH<sup>&#8722;</sup>]<sub>TOT</sub></nobr> =
<nobr>&#8722;5 mM</nobr> to simulate an initial solution
containing a strong acid, <nobr>[HCl]<sub>initial</sub></nobr> = 5 mM,
and 10 mM acetic acid. Compare
the diagram above with a titration curve without acetic acid
<nobr>(<a href="Tut_Titr_StrongAcid.htm">titration</nobr> of a strong acid with
a strong <nobr>base</a>).</nobr></p>

<p>You can simulate a tritration of a smaller amount of acetic acid, but
remember to decrease the X-axis range in the same proportion. For example,
for a titration of 1 mM of acid, the <nobr>[OH<sup>&#8722;</sup>]</nobr>
concentration should be between zero and  <nobr>&#8776;2</nobr> mM.
What is the minimum initial acid concentration required to &#147;see&#148; a pH
change? Is it possible, for example, to titrate a <nobr>1 &#956;M</nobr> solution?</p>

<a name="Mg-edta"></a>
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<h3>Titration of Mg with <i>edta</i></h3>

<p>
Magnesium can be titrated with <i>edta</i> using a pH 10 buffer and
<a href="Tut_Titr_Calmagite.htm">Calmagite</a> as metal-indicator.
This is a tri-protic acid, <nobr>H<sub>3</sub>ind,</nobr> and its colour changes
with protonation: <nobr>H<sub>2</sub>ind<sup>&#8722;</sup></nobr> is bright red
(pH &lt; 9),
<nobr>Hind<sup>2&#8722;</sup></nobr> is clear blue (pH 9 to 12), and
<nobr>ind<sup>3&#8722;</sup></nobr> is reddish orange (pH &gt; 12).
Complexation with Ca or Mg also induces a colour change (at pH 10):</p>

<table cellspacing="0" cellpadding="0">
 <tr valign="baseline">
  <td><tt>&nbsp;&nbsp;</tt></td>
  <td>Mg<sup>2+</sup></td>
  <td align="right">
  &nbsp;+&nbsp;<nobr>Hind<sup>2&#8722;</sup></nobr><br><font color="#0000FF"><b>blue</b></font>&nbsp;&nbsp;</td>
  <td>&nbsp;<img src="images/rlh.gif" alt="=" title="=" height="10" width="14" border="0">&nbsp;</td>
  <td align="center">
  <nobr>Mg(ind)<sup>&#8722;</sup></nobr><br><font color="#DC143C"><b>red</b></font>
  </td>
  <td>&nbsp;+&nbsp;<nobr>H<sup>+</sup></nobr></td>
  </tr>
</table>

<p>Because Calmagite is not included in the <a href="DB_0_Main.htm">DATABASE</a>
database you must <a href="DB_Add_data.htm">add the new data</a> for this indicator.
The original <a href="Tut_Titr_Calmagite.htm">reference</a> contains
some approximate equilibrium constants
(at <a href="SP_Ionic_Strength.htm">ionic strength</a> <i>I</i> = <nobr>0.1 M):</nobr></p>

<table cellspacing="0" cellpadding="0">
 <tr valign="baseline"><td><tt>&nbsp;&nbsp;</tt></td>
 <td><nobr>ind<sup>3&#8722;</sup></nobr> + <nobr>H<sup>+</sup></nobr>
    <img src="images/rlh.gif" alt="=" title="=" height="10" width="14" border="0">
    <nobr>Hind<sup>2&#8722;</sup></nobr></td>
  <td><tt>&nbsp;&nbsp;</tt></td>
  <td><nobr>log<i>K</i><sub>1,H</sub></nobr> = 12.35</td>
  </tr>
 <tr valign="baseline"><td><tt>&nbsp;&nbsp;</tt></td>
 <td><nobr>ind<sup>3&#8722;</sup></nobr> + <nobr>2H<sup>+</sup></nobr>
    <img src="images/rlh.gif" alt="=" title="=" height="10" width="14" border="0">
    <nobr>H<sub>2</sub>ind<sup>&#8722;</sup></nobr></td>
  <td><tt>&nbsp;&nbsp;</tt></td>
  <td><nobr>log<i>&#946;</i><sub>2,H</sub></nobr> = 20.49</td>
  </tr>
 <tr valign="baseline"><td><tt>&nbsp;&nbsp;</tt></td>
 <td><nobr>ind<sup>3&#8722;</sup></nobr> + <nobr>Mg<sup>2+</sup></nobr>
    <img src="images/rlh.gif" alt="=" title="=" height="10" width="14" border="0">
    <nobr>Mg(ind)<sup>&#8722;</sup></nobr></td>
  <td><tt>&nbsp;&nbsp;</tt></td>
  <td><nobr>log<i>K</i><sub>1,Mg</sub></nobr> = 5.7</td>
  </tr>
</table>
<p>The last equilibrium constant, <nobr><i>K</i><sub>1,Mg</sub>,</nobr> was
estimated in the reference from a meassured 25% &#147;extent of dissociation
of the compound&#148; at <i>I</i> = <nobr>0.1,</nobr> pH = 10 and
Calmagite and Mg concentrations equal to <nobr>2.5&times;10<sup>&#8722;5</sup></nobr>
M. Simulations made with <a href="S_0_Main.htm">Spana</a> show that
<nobr>log<i>K</i><sub>1,Mg</sub></nobr> must instead be <nobr>&#8776;7.4</nobr>
to obtain such degree of complex formation, and we will use this corrected value.</p>

<p>Extrapolation to zero ionic strength using
<a href="SP_Ionic_Strength.htm#Models">Davies eqn.</a> gives
<nobr>log<i>K</i>&deg;<sub>1,H</sub></nobr> <nobr>&#8776;13.02,</nobr>
<nobr>log<i>&#946;</i>&deg;<sub>2,H</sub></nobr> <nobr>&#8776;21.60,</nobr>
and
<nobr>log<i>K</i>&deg;<sub>1,Mg</sub></nobr> <nobr>&#8776;8.7.</nobr></p>

<p><a href="DB_Add_data.htm">Add these data</a> in DATABASE.</p>

<p>After that, to simulate a Mg-<i>edta</i> tritration start by selecting in DATABASE
the following components: <nobr>H<sup>+</sup>,</nobr> <nobr>Mg<sup>2+</sup>,</nobr>
<nobr>EDTA<sup>4&#8722;</sup>,</nobr> <nobr>NH<sub>3</sub></nobr> and
<nobr>Ind<sup>3&#8722;</sup></nobr> (which you have just added as a component).
Then use the menu &#147;File / Save and exit&#148; to make an input file for Spana.</p>

<p>When simulating a titration it is important to keep track of the proton balance.
<i>Edta</i> solutions are normally prepared from the di-sodium salt
<nobr>Na<sub>2</sub><i>edta</i>&middot;2H2O.</nobr>
In Spana select the menu &#147;Run&nbsp;/
<nobr><a href="S_Modify_Chem_System.htm">Modify chemical system</a>&#148;</nobr>
to exchange <nobr>EDTA<sup>4&#8722;</sup></nobr> for
<nobr>H<sub>2</sub>EDTA<sup>2&#8722;</sup>.</nobr></p>

<p>Exchange also <nobr>Ind<sup>3&#8722;</sup></nobr> for <nobr>HInd<sup>2&#8722;</sup></nobr>
and <nobr>H<sup>+</sup></nobr> for <nobr>NH<sub>4</sub><sup>+</sup></nobr>
(to simulate a <nobr>NH<sub>4</sub><sup>+</sup>/NH<sub>3</sub></nobr> pH&#8776;10 buffer).</p>

<p>Now a diagram can be made. Select <nobr>H<sub>2</sub>EDTA<sup>2&#8722;</sup></nobr>
for the X-axis, <nobr>[NH<sub>4</sub><sup>+</sup>]<sub>T</sub></nobr> = 0.001 and
<nobr>[NH<sub>3</sub>]<sub>T</sub></nobr> = 0.02 (to keep pH &#8776;10),
<nobr>[Mg<sup>2+</sup>]<sub>T</sub></nobr> = 0.001 and
<nobr>[HInd<sup>2&#8722;</sup>]<sub>T</sub></nobr> = <nobr>5&times;10<sup>&#8722;6</sup>.</nobr></p>

<p>The following fraction diagram for Calmagite species is obtained:
<center>
<img src="images/Titration_Mg-edta.gif" alt="Titration_Mg-edta" title="Titration_Mg-edta" height="239" width="309" border="1">
</center></p>
<p>The end point is reached when the solution is <b><font color="#0000FF">blue</font></b>
without a trace of <b><font color="#800080">purple</font></b> colour. By varying the
the concentration of the buffer <nobr>(NH<sub>3</sub>)</nobr> it is seen that
if pH is decreased below 10 then the fraction of <nobr>H<sub>2</sub>ind<sup>&#8722;</sup></nobr>
increases, the final colour becomes less <b><font color="#0000FF">blue</font></b>,
and the titration&rsquo;s end point is more difficult to see.</p>

<p>It may be shown, by making a fraction diagram for <nobr>Mg<sup>2+</sup>,</nobr>
that the initial solution is slightly oversaturated with <nobr>Mg(OH)<sub>2</sub>(cr)</nobr>,
and precipitation might occur at higher pH, and perhaps at higher Mg-concentrations.
This would make the colour change sluggish and the end point difficult to see.
In conclusion: the buffering of pH is fundamental
in this titration.</p>

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